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Slice Method

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1. Slice Method
2. Lecture 10. Slice methodLet’s pick out a sufficiently large layer of air
3. Lecture 10. Slice methodSlice method assumptions:all variations
4. Lecture 10. Slice methodThe latter means that
5. Lecture 10. Slice methodTo derive the stability criterion:
6. Lecture 10. Slice methodSuppose, particles come from lower level to upper one:
7. Lecture 10. Slice methodFrom (10.10)-(10.13) we obtain:
8. Lecture 10. Slice methodLet’s use (10.9)
9. Lecture 10. Slice methodLet’s consider 3 cases:Updraft
10. Lecture 10. Slice method2nd case:Updraft and downdraft
11. Lecture 10. Slice method3d case:Updraft air is saturated and downdraft flux is not.Cu clouds development
12. Lecture 10. Slice methodFrom (10.18)
13. Lecture 10. Slice methodLet’s introduce a critical lapse rate
14. Lecture 10. Slice methodat conditionally unstable stratification
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Lecture 10. Slice methodLet’s pick out a sufficiently large layer of air

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Слайд 1Lecture 10. Slice method
Lecture 10 part 2
1. Particle method (Lect. 8-9):
assumption

of particle motion within motionless environment.
2. Basic approaches of slice

method: 1938-1939 (Bjerknes J.,Petersen S., Shishkin N. )

Slice method

Lecture 10. Slice methodLecture 10 part 21. Particle method (Lect. 8-9):assumption of particle motion within motionless environment.2.

Слайд 2Lecture 10. Slice method
Let’s pick out a sufficiently large layer

of air

Lecture 10. Slice methodLet’s pick out a sufficiently large layer of air

Слайд 3Lecture 10. Slice method
Slice method assumptions:
all variations of the quantities

within the picked out layer come out adiabatically;
no advection (horizontal

mass motion) is observed;
the mass of air above any layer remains unchanged.

Lecture 10. Slice methodSlice method assumptions:all variations of the quantities within the picked out layer come out

Слайд 4Lecture 10. Slice method
The latter means that fluxes of air

mass through section S’ and S’’ are equal:

Lecture 10. Slice methodThe latter means that fluxes of air mass through section S’ and S’’ are

Слайд 5Lecture 10. Slice method
To derive the stability criterion:

Lecture 10. Slice methodTo derive the stability criterion:

Слайд 6Lecture 10. Slice method
Suppose, particles come from lower level to

upper one:

Lecture 10. Slice methodSuppose, particles come from lower level to upper one:

Слайд 7Lecture 10. Slice method
From (10.10)-(10.13) we obtain:

Lecture 10. Slice methodFrom (10.10)-(10.13) we obtain:

Слайд 8Lecture 10. Slice method
Let’s use (10.9)

Lecture 10. Slice methodLet’s use (10.9)

Слайд 9Lecture 10. Slice method
Let’s consider 3 cases:

Updraft and downdraft air

isn’t saturated

Criteria of stability of both methods (parcel and slice

ones) give the same result.

Lecture 10. Slice methodLet’s consider 3 cases:Updraft and downdraft air isn’t saturatedCriteria of stability of both methods

Слайд 10Lecture 10. Slice method
2nd case:

Updraft and downdraft air fluxes are

saturated

Criteria of stability of both methods (parcel and slice ones)

give the same result.

Lecture 10. Slice method2nd case:Updraft and downdraft air fluxes are saturatedCriteria of stability of both methods (parcel

Слайд 11Lecture 10. Slice method
3d case:

Updraft air is saturated and
downdraft

flux is not.

Cu clouds development

Lecture 10. Slice method3d case:Updraft air is saturated and downdraft flux is not.Cu clouds development

Слайд 12Lecture 10. Slice method
From (10.18)

and

Stability criteria of both methods are coincide if the stratification is absolutely unstable and absolutely stable. However, often

Lecture 10. Slice methodFrom (10.18)

Слайд 13Lecture 10. Slice method
Let’s introduce a critical lapse rate

Lecture 10. Slice methodLet’s introduce a critical lapse rate

Слайд 14Lecture 10. Slice method

at conditionally unstable stratification the atmosphere is

unstable for small size particles and it’s stable for LARGE

size particles =>>the atmospere is said to be selectively unstable

Lecture 10. Slice methodat conditionally unstable stratification the atmosphere is unstable for small size particles and it’s

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